Simplify; express your answer in exponential form. Assume $x\neq 0, q\neq 0$. $\dfrac{{x^{4}q^{5}}}{{(x^{2}q^{2})^{3}}}$
Answer: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${x^{4}q^{5} = x^{4}q^{5}}$ On the left, we have ${x^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${x^{4} = x^{4}}$ Apply the ideas above to simplify the equation. $\dfrac{{x^{4}q^{5}}}{{(x^{2}q^{2})^{3}}} = \dfrac{{x^{4}q^{5}}}{{x^{6}q^{6}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{4}q^{5}}}{{x^{6}q^{6}}} = \dfrac{{x^{4}}}{{x^{6}}} \cdot \dfrac{{q^{5}}}{{q^{6}}} = x^{{4} - {6}} \cdot q^{{5} - {6}} = x^{-2}q^{-1}$